A Fractal Model of HIV Transmission on Complex Sociogeographic Networks: Towards Analysis of Large Data Sets

Abstract

A paradigm of HIV (human immunodeficiency virus) transmission along very large ‘sociogeographic’ networks—spatially focused nets of social interaction—is extended to include fractal (dilationally self-similar) structures upon which a metric of ‘sociogeographic’ distance can be defined. It is conjectured that, by proper definition of such a metric, the complex filamentary structure of a spreading infection may be mapped onto a simple, radially expanding, relatively compact set, providing a more direct characterization of disease transmission. Inverse transformation then provides maps of disease dynamics in ‘real’ geographic and social spaces. Techniques are sketched for determining the sociogeographic structure of a large, geographically centered social network, providing a possible empirical basis for predicting forms and rates of spread of the initial, rapid, stages of an HIV outbreak for networks not yet infected, and perhaps greatly expanding the utility of routinely collected small-area administrative data sets in the design of mutually reinforcing, multifactorial disease-control strategies.